Secure CheckoutPersonal information is secured with SSL technology.
Free ShippingFree global shipping
No minimum order.
1. QUANTIZATION AND INTEGRABILITY
1.1 Algebraic and Geometric Methods
1.2 Vertex Operators and Coherent States
1.3 Remarks on the Olavo Theory
1.4 Trajectory Representations
2. GEOMETRY AND EMBEDDING
2.1 Curves and Surfaces
2.2 Surfaces in R3 and Conformal Immersion
2.3 Quantum Mechanics on Embedded Objects
2.4 Willmore Surfaces, Strings and Dirac
2.5 Conformal Maps and Curves
3. CLASSICAL AND QUANTUM INTEGRABILITY
3.2 R Matrices and PL Structures
3.3 Quantization and Quantum Groups
3.4 Algebraic Bethe Ansatz
3.5 Separation of Variables
3.6 Hirota Equations
3.7 SOV and Hitchin Systems
3.8 Deformation Quantization
3.10 Summary Remarks
4. DISCRETE GEOMETRY AND MOYAL
4.2 Hirota, Strings, and Discrete Surfaces
4.3 A Few Summary Remarks
4.4 More on Phase Space Discretization
5. WHITHAM THEORY
5.2 Isomonodromy Problems
5.3 Whitham and Seiberg-Witten
5.4 Soft Susy Breaking and Whitham
5.6 Whitham, WDVV, and Picard-Fuchs
6. GEOMETRY AND DEFORMATION QUANTIZATION
6.1 Noncommutative Geometry
6.2 Gauge Theories
6.3 Berezin Toeplitz Quantization
About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory.
- No. of pages:
- © North Holland 2000
- 9th November 2000
- North Holland
- eBook ISBN:
@qu:The book contains an impressive amount of information on topics such as integrable systems, quantum groups, different types of quantization, Whitham theory and non-communicative geometry. @source:Deutschen Mathematiker Vereinigung
University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Elsevier.com visitor survey
We are always looking for ways to improve customer experience on Elsevier.com.
We would like to ask you for a moment of your time to fill in a short questionnaire, at the end of your visit.
If you decide to participate, a new browser tab will open so you can complete the survey after you have completed your visit to this website.
Thanks in advance for your time.